System for quantifying blood flow in tissue and updating tissue baseline conditions

ABSTRACT

Methods and apparatus for determining blood flow in tissue are disclosed. The methods and apparatus are used to establish a baseline for both thermal properties of the tissue and non-physiologic conditions. Periodic changes in either or both constituents of the baseline are determined and, when the changes correspond to a need for a new baseline, a new baseline is established.

SUMMARY OF THE INVENTION

The present invention covers technology developed to provide clinicianswith a powerful prognostic tool for quantifying tissue blood flow (i.e.,“perfusion”) in continuous, real-time. The measurements made by theapparatus of the present invention have long been sought after andrepresent important parameters in the understanding and management ofmany critical medical situations, and prior to the development of thistechnology, the practical capability to get continuous, real-time, softtissue perfusion measurements in absolute units, did not exist. The highclinical value of the technology behind this invention has beendocumented in life-saving neurosurgical and organ transplantationsurgery cases, among others.

In the monitoring of perfusion in the tissue of a subject (i.e.: theflow of blood in a capillary bed) it is useful to have a continuous ornearly continuous stream of data over time. The accuracy of measurementsis affected by various physiologic and instrument baseline changes.Thus, it is also useful to monitor baseline conditions and adjust forbaseline shifts over time. The monitoring system surveys selectedbaseline factors that may adversely affect the integrity of themonitored data and uses the results to make corrections.

The continuous measurement of perfusion over time is valuable in manyclinical settings. Among them are the measurement of perfusion in thebrain of patients with traumatic brain injury to anticipate adverseconditions such as cerebral ischemia, the monitoring of perfusion inorgan transplantation to assess ischemia caused by thrombotic andreperfusion injury and the monitoring of perfusion in flaps inreconstructive plastic surgery to assess tissue viability. The perfusionvalue is also an indicator of the presence or absence of shock andmonitoring perfusion over time may permit the clinician to anticipateand treat shock.

Approximately 370,000 Americans suffer traumatic head injury annually.By using the apparatus of the present invention to measure continuous,real-time cerebral tissue blood flow, clinicians can identify patientsat risk for ischemia due to vasospasm or cerebral edema (brainswelling), and measure the patient's tissue blood flow response totherapies implemented to correct the pathology. In addition, othercritical neurosurgical interventions, such as aneurysm repair, tumor andarterial-veinous malfunction removal and procedures to relieve patientssuffering from subarachnoid hemorrhage are among those that will alsobenefit from the valuable prognostic data provided by the apparatus ofthe present invention.

One embodiment, the Bowman Perfusion Monitor, Model 500, is a devicethat monitors tissue blood flow continuously at the capillary level inreal-time and in absolute units of ml/100 g-min. The Model 500perfusion-monitoring device utilizes thermal diffusion technologydescribed here through its minimally invasive, QFlow 500 Probe, whichphysicians can implant in cerebral or any other soft tissue.

The present invention may be used over extended periods of time inliving subjects and provide thermal property and perfusion data with ahigh degree of accuracy. This obtains even when tissue physiology ischanging and the physiological changes are accompanied by changingthermal properties in the tissue. Thermal properties of particularinterest are the properties of diffusivity and conductivity which areuseful in the determination of tissue perfusion.

To accommodate physiological or non-physiological changes over time, thepresent invention provides methods and apparatus for determiningbaseline thermal conditions of the tissue at a selected location or siteand for establishing baseline criteria to be used for the periodicupdating of baseline tissue conditions (in situ calibration). Thebaseline tissue conditions or thermal properties may change with time.Thus, one or more steps are provided for periodically determining theneed for updating to new baseline tissue conditions (in siturecalibration) as tissue conditions change.

Calibration or the establishing of a baseline may also take into accountinternal monitoring system parameters (artifacts). Recalibration or theestablishing of a new baseline may include one or more steps forperiodically determining parameter changes and, when changes are outsideof an acceptable range, recognizing the need for new or updated baselinecriteria. Accordingly baseline criteria are updated as the parametersand conditions unintentionally change.

The process of establishing a new or updated baseline may be manuallyinitiated or the system may automatically self-adjust (i.e.:self-recalibrate). The instrument may self-adjust automatically andperiodically when physiology changes by some predetermined amount orwhen a combination of physiologic conditions and system parameterschange by a predetermined amount. The system monitors the parameters andconditions to determine when values have changed to be outsidepredetermined limits and recalculates baseline when limits are exceeded.

One embodiment of the present invention is directed to a method for theperiodic updating of tissue baseline conditions in order to makeperfusion measurements over extended periods during which tissuebaseline conditions change as a consequence of multiple physiologic andnon-physiologic factors. The method may comprise the following steps:(a) perform in situ calibration of a perfusion sensor in the tissue,that is, establish baseline tissue conditions; (b) make perfusionmeasurement in tissue and (c) automatically recognize conditions underwhich the in situ calibration is no longer valid. Examples of suchconditions include physiologic conditions such as tissue and vasculardamage, tissue edema, tissue scar formation, influence of a largevessel, change in vascular status, such as blood volume, vasodilation,and vasoconstriction; changes in perfusion; changes in blood pressure;changes in tissue pressure; changes in tissue temperature; changes inblood temperature; changes in tissue metabolism; and/or measurement ofartifact conditions, such as sensor motion relative to the tissue,excessive sensor-tissue contact force inducing capillary collapse,insufficient sensor-tissue contact force resulting in artifactualtransduction of perfusion, sensor cross-talk, ambient temperaturechanges, electrical interference, instrumentation drift. Following step(c), (d) automatically perform a recalibration, selected from one ormore of the following to reestablish baseline conditions; proberecalibration and instrumentation recalibration; and (e) repeat thesteps as necessary to maintain optimum operation.

BRIEF DESCRIPTION OF THE DRAWINGS

Certain preferred embodiments are described below with reference to theaccompanying figures in which:

FIG. 1 is a front view depiction of an embodiment of the invention.

FIG. 2 is a block diagram of an embodiment of a system in which thedisclosed techniques can be used.

FIG. 3 is a flow chart of one embodiment of the present invention.

FIG. 4 is a flow chart of a system to repeatedly recalibratethermal-based perfusion sensors.

FIG. 5 is a high-level general block diagram of a method for determiningproperties of a medium.

FIG. 6 is detailed block diagram of a method for determining propertiesof a medium.

FIG. 7 is a block diagram of an apparatus for determining the propertiesof a medium.

FIG. 8 is a simplified diagram of one embodiment of a circuit used in acontrol circuit.

FIG. 9 is a simplified diagram of one embodiment of another circuit usedin a control circuit.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

This invention can be implemented by use of a system such as shown inFIG. 1 and illustrated schematically in FIG. 2. FIG. 1 shows the BowmanPerfusion Monitor with a display screen 52, a keyboard 62, connector 53for a perfusion probe, a slot 63 to permit passage of a printed tape andan on/off switch 51. As explained in the Bowman patents referenced belowand illustrated by FIG. 2, a probe 10 is immersed in a medium (e.g.:tissue) 11 and can be heated by a heater voltage V_(h)(t) supplied viacontrol circuit 13. The sensed voltage V_(s)(t) from probe 10 issupplied to A/D converter 15 for supplying to a data processor 14 indigital form for suitable processing thereof in order to determine k(intrinsic thermal conductivity), α (diffusivity), and ω (flow rate orperfusion), the values of which can be displayed in a display device 16.The values of probe calibration constants k_(b), a, and R_(i) can besupplied via a suitable input unit that may be in the form of a memorychip. Such operation is essentially described in the aforesaid patentsfor a particular mathematical model described therein and the samesystem as generally depicted therein can also be used for a differentmathematical model, the processing equations required to be implementedin data processor 14 being different depending on the mathematical modelselected.

The method of determining properties of a medium by causing a thermalchange in the medium and then calculating it's properties based on themedium's response to the thermal change is described in detail in U.S.Pat. No. 4,059,982 to H. F. Bowman issued on Nov. 29, 1977; U.S. Pat.No. 4,852,027 to H. F. Bowman and W. H. Newman issued on Jul. 25, 1989and U.S. Pat. No. 5,035,514 to William H. Newman issued on Jul. 30,1991.

As illustrated in FIGS. 3 and 4, methods and software apparatus areprovided to repeatedly recalibrate thermal-based perfusion sensors andrelated instrumentation. The system monitors the conditions of theelectronic instrument and conditions affecting the sensor and, via thesensor, also monitors the conditions of tissue, organ and the overallphysiology of the subject to establish a baseline. When the weightedcombination of conditions in the instrument and sensor and in thephysiology of the subject fall outside a preset threshold, a perfusionmeasurement less accurate than desired is indicated and the systemdetermines that a new baseline (recalibration) is needed. The system maymonitor these conditions or use inputs from other devices that monitorphysiologic or instrument conditions. The establishment of a newbaseline (recalibration) may be initiated manually after the systemprompts the operator or it may be automatically initiated by the system.Similarly, the system may also be prompted by an external apparatus toautomatically perform part or all of the recalibration process.

The instrument conditions that are monitored include, but are notlimited to; ambient temperature changes, electrical interference, andinstrumentation drift. The thermal-based perfusion sensor conditionsthat are monitored include, but are not limited to; excessivesensor-tissue contact force that can result in capillary collapse,insufficient sensor-tissue contact force that can result in artifactualthermal transduction, sensor cross-talk, and movement of the sensorrelative to the tissue. The physiologic conditions of the subject thatare monitored include, but are not limited to; tissue and vasculardamage, tissue edema, tissue scar formation, influence of a largevessel, change in vascular status (i.e.: blood volume, vasodilation, andvasoconstriction), changes in perfusion, changes in blood pressure,changes in tissue pressure, changes in tissue temperature, changes inblood temperature, and changes in tissue metabolism.

According to certain embodiments of the invention a method fordetermining perfusion in living tissue includes the steps of: (1)establishing baseline tissue criteria by determining an unperturbedtemperature of the tissue, causing the temperature of the tissue tochange from a first unperturbed temperature to a second temperaturedifferent from said first temperature for a time period, and determininga value or values for one or more thermal properties of the tissueduring the time period; (2) calculating a perfusion value for the tissueduring the time period using said thermal property value or values, and(3) evaluating one or more physiological and artifactual conditions todetermine if previously established baseline criteria are materiallyaffected by said conditions. If previously established baseline criteriaare materially affected by changed conditions, (4) the first step isrepeated to establish new values for baseline thermal properties. Thethermal properties for which a value or values are determined mayinclude either or both of thermal conductivity and thermal diffusivity.

Certain embodiments of a method for measuring perfusion in tissuecomprise the steps of: (1) establishing a baseline criteria for tissueconditions, comprising the steps of: (A) determining an unperturbedtemperature of the tissue, (B) causing the temperature of said tissue tochange from a first unperturbed temperature to a second temperaturedifferent from said first temperature during a time period the initialportion of which is affected strongly by conductive factors and a secondportion of which is affected strongly by convective factors, (C)calculating an intrinsic thermal conductivity and a diffusivity of saidtissue during a first selected portion of said time period, (2)obtaining measurements of perfusion of the tissue comprising the stepsof: (A) calculating a perfusion of said tissue at a second selectedportion of said time period using said calculated intrinsic thermalconductivity and diffusivity, (B) re-calculating the intrinsic thermalconductivity and diffusivity of said tissue during said first selectedportion of said time period using said calculated perfusion, (C)re-calculating the perfusion of said tissue at said second selectedportion of said time period using said recalculated intrinsic thermalconductivity and diffusivity, and (D) repeating steps 2(B) and 2(C)until the re-calculated intrinsic thermal conductivity and diffusivityand the re-calculated perfusion each converge to a substantiallynon-changing value; (3) determining need for new baseline criteriacomprising evaluating physiological conditions that may affect baselinetemperature, conductivity and/or diffusivity values.

In certain embodiments step (3) further comprises the step of evaluatingmeasurement artifact conditions that may affect baseline temperature,conductivity and/or diffusivity values. Other embodiments furthercomprise a step (4) when new baseline criteria are indicated by step (3)for permitting the temperature of the tissue to relax to an unperturbedstate and then repeating step (1). In certain other embodiments step(1)(B) includes: activating said temperature changing means whenimmersed in said tissue to change the temperature of said tissue. Instill other embodiments step (1)(B) includes: immersing a cooling meansin said tissue; and applying power to said cooling means to cool saidtissue from said first unperturbed temperature. The intrinsic thermalconductivity and diffusivity of step (1)(C) are calculated at the firstselected portion of said time period when convective factors dominateand step (2)(A) is calculated at the second selected portion of saidtime period when conductive factors dominate.

In certain embodiments step (1)(B) includes: applying power to saidheating means while in contact with said tissue to heat said tissue fromsaid first unperturbed temperature to said second temperature. In otherembodiments the heating means has a substantially sphericalconfiguration and is of a type referenced in the previously mentionedU.S. Pat. Nos. 4,059,981 and 5,035,514. Said intrinsic thermalconductivity and diffusivity are calculated and recalculated in steps(1)(C) and (2)(B) and the perfusion is calculated and recalculated insteps (2)(A) and (2)(C) using the following equation:

$\begin{matrix}{{{P(t)} = {\frac{4\pi \; {ak}_{m}\Delta \; T}{\frac{1}{5\gamma} + \frac{1}{1 + {\lambda \; a}}}\left\lbrack {1 + \frac{\frac{a}{\sqrt{\pi \; a_{m}}}{f(t)}}{\frac{1 - {\lambda^{2}a^{2}}}{5\gamma} + 1 + {\lambda \; a}}} \right\rbrack}}{{V_{b}(t)} = {\Delta \; T}}{{P(t)} = 0}} & (i) \\{\frac{V_{b}(t)}{\Delta \; T} = {\frac{a/\sqrt{\pi \; \alpha_{m}}}{\frac{1 - {\lambda^{2}a^{2}}}{5\gamma} + 1 - {\lambda \; a}}\begin{bmatrix}{\left\{ {{f\left( {t - t_{heat}} \right)} - {f(t)}} \right\} +} \\\begin{matrix}\frac{a/\sqrt{{\pi\alpha}_{m}}}{\frac{1 - {\lambda^{2}a^{2}}}{5\gamma} + 1 + {\lambda \; a}} \\\frac{\sqrt{t_{heat}}^{{- \lambda}\; 2\alpha \; m^{t}}}{t\sqrt{t - t_{heat}}}\end{matrix}\end{bmatrix}}} & ({ii})\end{matrix}$

wherein P(t) is the power applied, a is the radius of the sphericalheating means, k_(m) and α_(m) are, respectively, the intrinsic thermalconductivity and thermal diffusivity of said tissue, γ is the ratiok_(b)/k_(m), k_(b) is the intrinsic thermal conductivity of thespherical heating means, λ is equal to √{square root over(wc_(m)/k_(m))}, where w is perfusion and c_(m) is the specific heat ofthe perfusate, V_(b) is the bead mean volumetric temperature duringcooling, ΔT is the volume averaged constant temperature change duringthe heating phase, t_(heat) is the length of time for which heating isapplied and f(t) represents the temporal form of the transient powerapplied to said heating means as a function of time.

Other variations, include but are not limited to, where said heatingmeans has a substantially spherical configuration and said intrinsicthermal conductivity and diffusivity are calculated and recalculated insteps (1)(C) and (2)(B) and the perfusion is calculated and recalculatedin steps (2)(A) and (2)(C) using the following equation:

$\begin{matrix}{{P = P_{o}}{and}} & \; \\{{{V_{b}(t)} = {\frac{P_{o}}{4\pi \; {ak}_{a}}\left\lbrack {\frac{1}{5\gamma} + \frac{1}{1 + {\lambda \; a}} - {\frac{a/\sqrt{{\pi\alpha}_{m}}}{1 - {\lambda^{2}a^{2}}}{f(t)}}} \right\rbrack}}{P = 0}} & ({iii}) \\{{V_{b}(t)} = {\frac{P_{o}}{4\pi \; {ak}_{a}\sqrt{{\pi\alpha}_{m}}}{\frac{1}{1 - {\lambda^{2}a^{2}}}\left\lbrack {{f\left( {t - t_{heat}} \right)} - {f(t)}} \right\rbrack}}} & ({iv})\end{matrix}$

wherein P_(o) is the constant power applied during the heating phase, ais the radius of the spherical heating means, k_(m) and α_(m) are,respectively, the intrinsic thermal conductivity and thermal diffusivityof said tissue, γ is the ratio k_(b)/k_(m), k_(b) is the intrinsicthermal conductivity of the spherical heating means, λ is equal to√{square root over (wc_(m)/k_(m))}, where w is perfusion and c_(f) isthe specific heat of the perfusate, V_(b) is the bead mean volumetrictemperature during a cool-down period, t_(heat) is the length of timefor which heating is applicated and f(t) represents the temporal form ofthe transient power applied to said heating means as a function of time.

In accordance with certain embodiments, a method for determining thermalproperties of a medium comprises the steps of: (A) establishingreference parameters for measuring, comprising determining unperturbedtemperature of medium; (B) obtaining measurements of medium comprisingthe steps of: (1) causing the temperature of said medium to change froma first unperturbed temperature to a second temperature different fromsaid first temperature during an overall time period, (2) calculatingeffective thermal conductivity and diffusivity values of said mediumduring a plurality of time periods within said overall time period, (3)extrapolating the effective thermal conductivity and diffusivity valuescalculated in step (2) to the thermal conductivity and diffusivityvalues at a selected time t_(o) when the temperature of said medium isfirst caused to change so as to determine the extrapolated values of theintrinsic thermal conductivity and diffusivity of said medium, (4)calculating a perfusion of said medium during a selected time period ofsaid overall time period using said extrapolated intrinsic thermalconductivity and diffusivity, (5) recalculating the effective thermalconductivity and diffusivity values of said medium during said pluralityof time periods; using said calculated perfusion, (6) re-extrapolatingthe thermal conductivity and diffusivity values recalculated in step (5)to the intrinsic thermal conductivity and diffusivity values at saidselected time t_(o), (7) recalculating the perfusion of said mediumduring said selected time period using the intrinsic thermalconductivity and diffusivity values reextrapolated in step (6); and (8)repeating steps (5) through (7) until the recalculated intrinsic thermalconductivity and diffusivity values and the recalculated perfusion valueconverge to substantially non-changing values; (C) determining the needfor new reference parameters for medium.

In certain preferred embodiments the temperature change produced in saidmedium is constant and further wherein in steps (2) and (5) the thermalconductivity and diffusivity are calculated in accordance with thefollowing equation:

${P(t)} = {\frac{4\pi \; {ak}_{a}\Delta \; T}{\frac{1}{5\gamma} + \frac{1}{1 + {\lambda \; a}}}\left\lbrack {1 + \frac{\frac{a}{\sqrt{\pi \; a_{a}}}{f(t)}}{\frac{1 - {\lambda^{2}a^{2}}}{5\gamma} + 1 + {\lambda \; a}}} \right\rbrack}$

In other embodiments the temperature change produced in said medium isconstant and further wherein in steps (4) and (7) the perfusion iscalculated in accordance with the following equation:

${P(t)} = {\frac{4\pi \; {ak}_{a}\Delta \; T}{\frac{1}{5\gamma} + \frac{1}{1 + {\lambda \; a}}}\left\lbrack {1 + \frac{\frac{a}{\sqrt{\pi \; a_{a}}}{f(t)}}{\frac{1 - {\lambda^{2}a^{2}}}{{5\gamma}\;} + 1 + {\lambda \; a}}} \right\rbrack}$

In still other embodiments the temperature change produced in saidmedium is constant and further wherein in step (4) and (7) the perfusionis calculated in accordance with the following equation, for a timeperiod which is subsequent to the deactivation of the temperaturechanging means:

$\frac{V_{b}(t)}{\Delta \; T} = {\frac{a/\sqrt{{\pi\alpha}_{m}}}{\frac{1 - {\lambda^{2}a^{2}}}{5\gamma} + 1 - {\lambda \; a}}\begin{bmatrix}{\left\{ {{f\left( {t - t_{heat}} \right)} - {f(t)}} \right\} +} \\\frac{a/\sqrt{{\pi\alpha}_{m}}}{\frac{1 - {\lambda^{2}a^{2}}}{5\gamma} + 1 + {\lambda \; a}} \\\frac{\sqrt{t_{heat}}^{{- \lambda}\; 2\alpha \; m^{t}}}{t\sqrt{t - t_{heat}}}\end{bmatrix}}$

Other embodiments have the temperature change in said medium produced byactivating a power source so as to produce a change in power which isconstant and further wherein in steps (2) and (5) the thermalconductivity and diffusivity are calculated in accordance with thefollowing equation:

${V_{b}(t)} = {\frac{P_{o}}{4\pi \; {ak}_{a}}\left\lbrack {\frac{1}{5\gamma} + \frac{1}{1 + {\lambda \; a}} - {\frac{a/\sqrt{{\pi\alpha}_{m}}}{1 - {\lambda^{2}a^{2}}}{f(t)}}} \right\rbrack}$

The temperature change in said medium may also be produced by activatinga power source so as to produce a change in power which is constant andfurther wherein in steps (4) and (7) the perfusion is calculated inaccordance with the following equation:

${V_{b}(t)} = {\frac{P_{o}}{4\pi \; {ak}_{a}}\left\lbrack {\frac{1}{5\gamma} + \frac{1}{1 + {\lambda \; a}} - {\frac{a/\sqrt{{\pi\alpha}_{m}}}{1 - {\lambda^{2}a^{2}}}{f(t)}}} \right\rbrack}$

Other embodiments have the temperature change in said medium produced byactivating a power source so as to produce a change in power which isconstant and further wherein in steps (4) and (7) the perfusion iscalculated in accordance with the following equation, for a time periodwhich is subsequent to the deactivation of the power source:

${V_{b}(t)} = {\frac{P_{o}}{4\pi \; {ak}_{a}\sqrt{{\pi\alpha}_{m}}}{\frac{1}{1 - {\lambda^{2}a^{2}}}\left\lbrack {{f\left( {t - t_{heat}} \right)} - {f(t)}} \right\rbrack}}$

FIG. 2 depicts a block diagram of showing the basic steps of the abovementioned methods.

In the embodiment illustrated by FIG. 5, step (1) consists ofdetermining baseline conditions in the medium and establishing baselinecriteria based thereon. This step can involve numerous steps but thebasic purpose is to establish a reference for the medium that allfollowing measurements will be compared against. The criteria can comefrom the probe of the measuring device, can be user inputted, orobtained from other instrumentation. This step may also include the stepof calibrating the instrumentation used; that is, establishing baselinecriteria for the instrumentation.

Step (2) comprises of obtaining measurements of the medium, for example,live tissue. In a preferred embodiment this comprises raising thetemperature of the medium and monitoring the time, and power required toraise and then maintain the new temperature. In some cases this step mayalso include ceasing to heat the medium and monitoring the cool downrate. From this process properties of the medium such as thermalconductivity and rate of flow can be calculated. These measurements andcalculations may be performed multiple times.

Step (3) comprises determining if new baseline criteria need to beestablished. In a preferred embodiment the baseline conditions on whichbaseline criteria are based are monitored thru-out the method. If thereis a change indicating that conditions of the medium or other conditionson which baseline criteria are based have changed, calculations andmeasurements based on the original baseline conditions may no longer bevalid. Therefore it may be necessary to obtain a new baseline. Incertain embodiments step (3) comprises the steps of: comparingmeasurements taken and calculated to established baseline criteria toexisting measurements and determining if there has been a change inconditions. In other embodiments step (3) comprises the steps ofcomparing measurements received from other instrumentation to baselinecriteria, and determining if there has been a change in conditions.

In certain embodiments the methods have an additional step (4)consisting of repeating the process again if new baseline criteria arerequired. This includes establishing new baseline criteria and obtainingnew measurements based on the new baseline criteria.

In accordance with certain embodiments, a method for determiningproperties of a medium comprises the steps of: determining baselineconditions and establishing baseline criteria for the medium; inducing atemperature change in the medium during a predetermined interval;calculating at least one selected intrinsic thermal property of saidmedium using data obtained at a first time period; calculatingseparately a perfusion rate of said medium using data obtained at asecond time period and said at least one calculated intrinsic thermalproperty, the effects of the perfusion of said medium at said secondtime period being greater than the effects of the perfusion of saidmedium at said first time period; and determining the need for newbaseline criteria for the medium. The invention may further compriserepeating the previous steps to obtain another perfusion rate of themedium when need for a new baseline is indicated.

In accordance with certain other embodiments, a method for determiningproperties of a medium with automatic recalibration comprises thesteps: 1) measuring the temperature of the medium at a first and secondlocation; 2) determining if the temperatures at the first and secondlocation are stable, wherein if the temperature at either the first orsecond location are not stable then repeating step 1; 3) raising thetemperature of the medium at the second location a predetermined amount;4) measuring the temperature at the first location and calculating thepower required to raise the temperature at the second location; 5)repeating step 4 for a set period of time; 6) calculating the intrinsicthermal conductivity of the medium; 7) calculating the rate of flow ofthe medium; 8) determining if the temperature of the medium at the firstlocation is stable, wherein if the temperature at the first location isnot stable, then repeating step 1; 9) determining if the change in powerover time is less than an established maximum value, wherein if thechange in power over time is not less than the established maximum, thenrepeating step 1; 10) determining if the total time the measurementshave been taken over is less than an established maximum, wherein if thetotal is not less than the established maximum, then repeating step 1;11) repeating step 4.

In accordance with one embodiment, in a method for determiningproperties of a medium comprising the steps of: (1) causing thetemperature of said medium to change from a first unperturbedtemperature to a second temperature different from said firsttemperature during a first time period; (2) causing the temperature ofsaid medium to relax to a final unperturbed temperature during a secondtime period; (3) calculating an intrinsic thermal conductivity and adiffusivity of said medium during a first selected portion of said firstand second time periods; (4) calculating a perfusion of said medium at,at least a second selected portion of said first and second timeperiods, using said calculated intrinsic thermal conductivity anddiffusivity; (5) recalculating the intrinsic thermal conductivity anddiffusivity of said medium during said first selected portion of saidfirst and second time periods using said calculated perfusion; (6)recalculating the perfusion of said medium at least at said secondselected portion of said first and second time periods using saidrecalculated intrinsic thermal conductivity and diffusivity; and (7)repeating steps (5) and (6) until the recalculated intrinsic thermalconductivity and diffusivity and the recalculated perfusion eachconverge to a substantially non-changing value; an improvement comprisesthe steps of: (a) prior to step (1), establishing baseline criteria thatcorrespond to properties of the medium; and (b) periodically determiningthe need for and establishing new baseline criteria.

In accordance with certain embodiments, represented by the block diagramof FIG. 5, a method for determining properties of a medium comprises thesteps of: (1) establishing baseline criteria for medium conditions orproperties, comprising: determining the thermal conductivity of aheating means, said heating means having a predetermined resistanceversus temperature relationship, and determining the referencetemperature of said medium when said heating means is immersed in saidmedium and said medium is unheated; (2) obtaining measurements of mediumcomprising the steps of: applying power to said heating meanssufficiently rapidly to heat said means to a volume mean temperatureabove said reference temperature so that the power necessary to maintainsaid volume mean temperature varies as a function of time, determiningthe time varying relationship between the power required to maintainsaid heating means at said volume mean temperature after saidtemperature has been reached and the time during which said power isbeing applied thereto, determining the temperature difference betweensaid volume mean temperature and said reference temperature anddetermining the resistance of said heating means at said volume meantemperature, determining the thermal conductivity of said medium as afunction of said temperature difference, of the resistance of saidheating means at said volume mean temperature, of said applied power inaccordance with said time varying power and time relationship, of saidpredetermined thermal conductivity of said heating means, and of atleast one characteristic dimension of said heating means in accordancewith a thermal model of said heating means and said medium in which itis immersed wherein said heating means is treated as a distributedthermal mass and wherein heat conduction occurs in a coupled thermalsystem which comprises both the heating means and the adjacent region ofsaid medium which surrounds said heating means; and (3) determining needfor new baseline criteria comprising evaluating physiological conditionsthat may materially affect the baseline criteria. Examples ofphysiological conditions include but are not limited to tissue andvascular damage, tissue edema, tissue scar formation, influence of alarge vessel, change in vascular status such as blood volume,vasodilation, and vasoconstriction; changes in perfusion, changes inblood pressure, changes in tissue pressure, changes in tissuetemperature, changes in blood temperature, and changes in tissuemetabolism.

In certain preferred embodiments step (3) further comprises the step ofevaluating measurement artifact conditions that may materially affectthe baseline criteria. Examples of measurement artifact conditionsinclude but are not limited to sensor motion relative to the tissue,excessive sensor such as tissue contact force or capillary collapse,insufficient sensor-tissue contact force such as artifactualtransduction of perfusion, sensor cross-talk, ambient temperaturechanges, electrical interference, instrumentation drift, automaticallyperform a recalibration, probe recalibration, and instrumentationrecalibration. In other embodiments the method further comprises step(4): repeating steps (1) and (2) when indicated by step (3).

In a certain preferred embodiment, in step (1), said referencetemperature is determined over a relatively short time period over whichit remains substantially constant and step (2) further including thesteps of: maintaining said volume mean temperature at a fixed,predetermined value above said reference temperature, said time varyingpower and time relationship being determined in terms of therelationship between the square of the voltage applied to said heatingmeans and the inverse square root of the time during which said voltageis being applied; determining a first characteristic Γ of saidrelationship representing the value of the power per unit volumegenerated by the heating means at a time t effectively equivalent to aninfinite time period following the application of said power to saidheating means; and further wherein said thermal conductivity of saidmedium is determined in accordance with the expression:

$k = \frac{5}{\frac{15\; \Delta \; T}{\Gamma \; \overset{\_}{a^{2}}} - \frac{1.0}{k_{b}}}$

where k is the thermal conductivity of said medium, ΔT is the said fixedvolume mean temperature difference, ā is the radius of a sphericalheating means having a volume equivalent to the actual volume of saidheating means, and k_(b) is said predetermined thermal conductivity ofsaid heating means.

In still other embodiments, in step (1), the step of determining saidreference temperature includes the steps of: measuring the voltage atsaid heating means in its unheated state; determining the currentthrough said heating means in its unheated state; determining theresistance of said heating means in its unheated state; and determiningsaid reference temperature in accordance with the said predeterminedresistance versus temperature relationship of said heating means.

In another embodiment according to step (2), the step of maintainingsaid volume mean temperature at said fixed value further includes thesteps of: preselecting a fixed value for said temperature difference;determining said volume mean temperature from said reference temperatureand said preselected fixed temperature difference; determining theresistance of said heating means at said volume mean temperature inaccordance with said predetermined resistance versus temperaturerelationship; and maintaining the resistance of said heating means at asubstantially constant value equal to said determined resistance wherebysaid volume mean temperature remains at a substantially constant value.

In another embodiment wherein the time varying relationship between thesquare of the voltage V_(h) ² and the inverse square root of the timet^(−1/2) is a substantially linear relationship of the form V_(h)²(t)=m₁+m₂t^(−1/2); and further wherein said first characteristic Γ isdetermined in accordance with the expression:

$\Gamma = \frac{m_{1}}{R_{h}\frac{4}{3}{\pi \left( \overset{\_}{a} \right)}^{3}}$

Other embodiments further include the steps of: predetermining thethermal diffusivity of said heating means; determining a secondcharacteristic β representing the slope of the time varying relationshipbetween the square of the voltage ν_(h) ² and the inverse square root ofthe time t^(−1/2) at a time relatively shortly after the time at whichsaid power is applied; predetermining the non-dimensional relationshipbetween the expression β√{square root over (α_(b))}/Γā wherein α_(b) isthe predetermined thermal diffusivity of said heating means; theexpression k_(m)/k_(b), wherein k_(m) is the thermal conductivity ofsaid medium with no fluid flowing therein; and the expressionα_(b)/α_(m) where α_(m) is thermal diffusivity of any medium which is tobe determined; determining the actual value of β√{square root over(α_(b))}/Γā and k_(m)/k_(b) at said volume mean temperature and furtherdetermining the value of α_(b)/α_(m) in accordance with saidpredetermined non-dimensional relationship; and determining the thermaldiffusivity α_(m) of said medium in accordance with the determined valueof α_(b)/α_(m).

In certain preferred embodiments time varying relationship between thesquare of the voltage V_(h) ² and the inverse square root of timet^(−/2) is a substantially linear relationship of the form V_(h)²(t)=m₁+m₂t^(−1/2); and further wherein said first characteristic Γ isdetermined in accordance with the expression:

${\Gamma = \frac{m_{1}}{R_{h}\frac{4}{3}{\pi \left( \overset{\_}{a} \right)}^{3}}};$

andsaid second characteristic β is determined in accordance with theexpression:

$\beta = \frac{m_{2}}{R_{h}\frac{4}{3}{\pi \left( \overset{\_}{a} \right)}^{3}}$

In other embodiments the reference temperature varies with time over arelatively long time period and further including the steps of:determining said reference temperature value over said time period;maintaining said volume mean temperature at a fixed, predeterminedvalue, said fixed value being greater than said reference temperatureover said time period; determining the time-varying temperaturedifference between said fixed volume mean temperature and saidtime-varying reference temperature; determining the fixed value of theresistance of said heating means at said volume mean temperature; anddetermining the thermal conductivity of said medium over said timeperiod in accordance with the expression:

${k(t)} = \frac{5}{\frac{\Delta \; {T(t)}R_{h}20\; \pi \; \overset{\_}{a}}{V_{h}^{2}(t)} - \frac{1.0}{k_{b}}}$

where k(t) is the thermal conductivity of said medium, ΔT is saidtemperature difference, R_(h) is the said fixed resistance of saidheating means at said volume mean temperature, a is the radius of aspherical heating means having a volume equivalent to the actual volumeof said heating means, V_(h)(t) is the voltage at said heating meanswhere said power is applied, and k_(b) is said predetermined thermalconductivity of said heating means.

In some embodiments the step of determining said reference temperatureincludes the steps of: immersing a temperature sensing means in saidmedium at a region sufficiently remote from the immersed heating meansso that the temperature sensed by said sensing element is not materiallyaffected by the raised temperature of said heating means, said sensingmeans having a predetermined resistance versus temperature relationship;determining over said time period the voltage at said sensing means andthe current through said sensing means; determining the referencetemperature sensed by said sensing means over said time period inaccordance with the said predetermined resistance versus temperaturerelationship thereof.

In another embodiment, the steps thereof are first performed when nofluid is flowing in said medium to determine the intrinsic thermalconductivity k_(m) of said medium and said steps are further performedover said time period when a fluid having a predetermined heat capacityis flowing in said medium to determine the effective thermalconductivity k_(eff)(t) of said medium; and further including the stepsof: predetermining the heat capacity C_(b) of said fluid; determiningthe ratio of k_(eff)(t)k_(m) over said time period; and determining therate of flow ω(t) of said fluid in said medium in accordance with theexpression:

${\omega (t)} = {\left( {\frac{k_{eff}(t)}{k_{m}} - 1} \right)^{2}\frac{k_{m}}{{C_{b}\left( \overset{\_}{a} \right)}^{2}}}$

where ω(t) is measured in terms of the mass of fluid per unit volume ofthe medium per unit time.

In another embodiment the reference temperature varies with time over arelatively long time period and further including the steps of:determining said reference temperature over said time period;determining the said volume mean temperature over said time period as afunction of said reference temperature and a preselected fixed value ofsaid temperature difference; maintaining the resistance of said heatingmeans over said time period at a value such as to maintain thetemperature difference between said volume mean temperature and saidreference temperature at said preselected fixed value, said resistancevarying as a function of time; determining the thermal conductivity k(t)of said medium over said time period in accordance with the expression:

${k(t)} = \frac{5}{\frac{\Delta \; {T(t)}R_{h}20\; \pi \; \overset{\_}{a}}{V_{h}^{2}(t)} - \frac{1.0}{k_{b}}}$

where ΔT is said temperature difference, R_(h)(t) is said resistance ofsaid heating means at said volume mean temperature, ā is the radius of aspherical heating means having a volume equivalent to the actual volumeof said heating means, V_(h)(t) is the voltage at said heating meanswhen said power is applied and k_(b) is the predetermined thermalconductivity of said heating means.

In another embodiment, the step of determining said referencetemperature includes the steps of: immersing a temperature sensing meansin said medium at a region sufficiently remote from the immersed heatingmeans so that the temperature sensed by said sensing element is notmaterially affected by the raised temperature of said heating means(referred to as sensor cross-talk), said sensing means having apredetermined resistance versus temperature relationship; determiningover said time period the voltage at said sensing means and the currentthrough said sensing means; determining the reference temperature sensedby said sensing means over said time period in accordance with the saidpredetermined resistance versus temperature relationship thereof.

In still other embodiments the steps thereof are first performed when nofluid is flowing in said medium to determine the intrinsic thermalconductivity k_(m) of said medium and said steps are further performedover said time period when a fluid having a predetermined heat capacityis flowing in said medium to determine the effective thermalconductivity k_(eff)(t) of said medium; and further including the stepsof: predetermining the heat capacity C_(b) of said fluid; determiningthe ratio of k_(eff)(t)/k_(m) over said time period; and determining therate of flow ω(t) of said fluid in said medium in accordance with theexpression:

${\omega (t)} = {\left( {\frac{k_{eff}(t)}{k_{m}} - 1} \right)^{2}\frac{k_{m}}{{C_{b}\left( \overset{\_}{a} \right)}^{2}}}$

where ω(t) is measured in terms of the mass of the fluid per unit volumeof the medium per unit time.

In another embodiment, the reference temperature varies with time over arelatively long time period and further including the steps of:immersing a temperature sensing means in said medium at a regionsufficiently remote from the immersed heating means so that thetemperature sensed by said sensing element is not affected by the raisedtemperature of said heating means, said sensing means having apredetermined resistance versus temperature relationship; determiningthe resistance of said sensing means over said time period; determiningthe reference temperature of said sensing means over said time period;determining the desired resistance of said heating means over said timeperiod as a function of the resistance of said sensing means and of apreselected fixed value of the resistance difference between theresistances of said sensing means and said heating means; maintainingthe resistance of said heating means at said desired resistance valueover said time period so that said resistance difference remains at saidpreselected fixed value, the resistance of said heating means varying asa function of time; determining the mean temperature of said heatingmeans over said time period at the said desired resistance value of saidheating means, said mean temperature varying as a function of time;determining the temperature difference between said mean temperature andsaid reference temperature over said time period, said temperaturedifference varying as a function of time; determining the thermalconductivity k(t) of said medium over said time period in accordancewith the expression:

${k(t)} = \frac{5}{\frac{\Delta \; {T(t)}R_{h}20\; \pi \; \overset{\_}{a}}{V_{h}^{2}(t)} - \frac{1.0}{k_{b}}}$

where ΔT(t) is said temperature difference, R_(h)(t) is said resistanceof said heating means at said mean temperature, a is the radius of aspherical heating means having a volume equivalent to the actual volumeof said heating means, V_(h)(t) is the voltage at said heating meanswhen said power is applied and k_(b) is the predetermined thermalconductivity of said heating means.

In another embodiment, the step of determining said referencetemperature includes the steps of: immersing a temperature sensing meansin said medium at a region sufficiently remote from the immersed heatingmeans to that the temperature sensed by said sensing element is notaffected by the raised temperature of said heating means (i.e.: nosensor cross-talk), said sensing means having a predetermined resistanceversus temperature relationship; determining over said time period thevoltage at said sensing means and the current through said sensingmeans; determining the reference temperature sensed by said sensingmeans over said time period in accordance with the said predeterminedresistance versus temperature relationship thereof.

In other embodiments, the steps thereof are first performed when nofluid is flowing in said medium to determine the intrinsic thermalconductivity k_(m) of said medium and said steps are further performedover said time period when a fluid having a predetermined heat capacityis flowing in said medium to determine the effective thermalconductivity k_(eff)(t) of said medium; and further including the stepsof: predetermining the heat capacity C_(b) of said fluid; determiningthe ratio of k_(eff)(t)/k_(m) over said time period; and determining therate of flow of said fluid in said medium in accordance with theexpression:

${\omega (t)} = {\left( {\frac{k_{eff}(t)}{k_{m}} - 1} \right)^{2}\frac{k_{m}}{{C_{b}\left( \overset{\_}{a} \right)}^{2}}}$

where ω(t) is measured in terms of the mass of the fluid per unit volumeof medium per unit time.

A more specific preferred embodiment can be seen in the block diagram ofFIG. 6 wherein the method comprises the steps of 1) measuring T1 and T2,the temperatures at a first and second location; 2) determining if T1and T2, the temperatures at the first and second locations are stable;3) if T1 and T2 are not stable, then repeating step 1; 4) if T1 and T2are stable, then setting T2 to a different temperature, T2+DT; 5)measuring T1 and calculating P2, the power required to change thetemperature at the second location; 6) determining if P2 data has beenacquired for a selected time period (i.e.: 10 seconds); 7) if 10 secondsof P2 data not acquired, then repeat step 5; 8) if 10 seconds of P2 datahas been acquired, then calculating intrinsic thermal conductivity ofthe medium, Km; 9) calculating perfusion, w; 10) determining if T1 isstable; 11) if T1 is not stable, then repeating step 1; 12) if T1 isstable, then determining if dP2/dt is less than dP/dt(max); 13) ifdP2/dt is not less than dP/dt(max), then repeating step 1; 14) if dP2/dtis less than dP/dt(max), then determining if time, t, is less thanestablished maximum time, t(max); 15) if t is not less than t(max), thenrepeating step 1; 16) if t is less than t(max), then repeating step 5.

In another embodiment, a method for determining properties of a mediumcomprises the steps of (1) establishing baseline criteria correspondingto baseline conditions of the medium, comprising: determining thethermal conductivity of a heating means as a function of temperature,said heating means having a predetermined resistance versus temperaturerelationship; contacting said medium with said heating means; anddetermining the reference temperature of said medium when said medium isunheated; (2) obtaining measurements of medium comprising the steps ofapplying power to said heating means sufficiently rapidly to heat saidmeans to a temperature above said reference temperature so that thepower necessary to maintain said temperature varies as a function oftime; determining the time varying power and time relationship betweenthe power required to maintain said temperature and the time duringwhich said power is applied to said heating means; determining thetemperature difference between said temperature and said reference;determining the thermal conductivity of said medium as a function ofsaid temperature difference, and of said applied power in accordancewith said time varying power and time relationship; and (3) determiningneed for new baseline criteria comprising evaluating physiologicalconditions and/or artifact conditions changes in which may affect thebaseline conditions of the medium.

Referring to FIG. 7, a method for determining properties of a mediumwith automatic recalibration comprises the steps of: 1) providing anapparatus for determining properties of a medium, comprising: a computer50, a display 52 in electrical communication with the computer, adetector circuit 54 in electrical communication with the computer 50, aprinter 56 in electrical communication with the detector circuit 54, afirst power supply 58 in electrical communication with the detectorcircuit 54, a second power supply 60 in electrical communication withthe computer 50, display 52, detector circuit 54, and printer 56; akeypad 62 in electrical communication with the detector circuit 54, anda probe 64 in electrical communication with the detector circuit 54; 2)inserting the probe into the medium; 3) having/operating the deviceperform the following steps: A) measuring the temperature of the mediumat a first and second location; B) determining if the temperatures atthe first and second location are stable, wherein if the temperature ateither the first or second location are not stable then repeating step1; C) raising the temperature of the medium at the second location apredetermined amount; D) measuring the temperature at the first locationand calculating the perfusion at the second location; E) repeating stepD for a set period of time; F) calculating the intrinsic thermalconductivity of the medium; G) calculating the rate of flow of themedium; H) determining if the temperature of the medium at the firstlocation is stable, wherein if the temperature at the first location isnot stable, then repeating step 1; I) determining if the rate ofperfusion is less than an established maximum value, wherein if rate ofperfusion is not less than the established maximum, then repeating stepA; J) determining if the total time the measurements have been takenover is less than an established maximum, wherein if the total is notless than the established maximum, then repeating step A; K) repeatingstep D.

In accordance with further embodiments, an apparatus for determiningphysical characteristics of a medium is provided. One such apparatuscomprises: temperature sensing means immersed in or contacting themedium for sensing the reference temperature of the medium when themedium is unheated; heating means immersed in the medium for heating themedium, the heating means having a predetermined thermal conductivity, apredetermined thermal diffusivity and a predetermined characteristicdimension; means for applying power to the heating means sufficientlyrapidly to raise the temperature of the heating means to a volume meantemperature above the reference temperature so that the power necessaryto maintain the volume mean temperature varies as a function of time;data processing means for determining the temperature difference betweenthe volume mean temperature and the reference temperature, fordetermining the resistance of the heating means at the volume meantemperature and for determining the time varying relationship betweenthe power required to maintain the heating means at the volume meantemperature after the temperature has been reached and the time duringwhich the power is being applied thereto; the data processing meansfurther being responsive to the temperature difference, the heatingmeans resistance, the applied power in accordance with the time varyingpower and time relationship, the predetermined thermal conductivity ofthe heating means, a change in reference parameters, and thepredetermined characteristic dimension of the heating means fordetermining the thermal conductivity of the medium in accordance with athermal model of the heating means and the medium wherein the heatingmeans is treated as a distributed thermal mass and wherein heatconduction occurs in a coupled thermal system which comprises both theheating means and the adjacent region of the medium which surrounds theheating means.

In certain embodiments the sensing means and the heating means comprisesa single element capable of sensing the temperature of the medium and ofheating the medium. An example of such a single element is a thermistorbead element, for example, of the type having characteristics referencedin above-mentioned U.S. Pat. Nos. 4,059,982 and 4,852,027. In otherembodiments the apparatus further includes volume means for maintainingthe mean temperature at a fixed, predetermined value above the referencetemperature, the reference temperature being determined and the volumemean temperature being maintained over a relatively short time intervalduring which the reference temperature remains substantially constantwhereby the temperature difference and the resistance of the heatingmeans also remain substantially constant. Variations of such anembodiment further include: means for determining the time varying powerand time relationship in terms of the relationship between the square ofthe voltage applied to the heating means and the inverse square root ofthe time during which the voltage is being applied; means fordetermining a first characteristic Γ of the relationship representingthe value of the power per unit volume generated by the heating means ata time t effectively equivalent to an infinite time period following theapplication of the power to the heating means; and means for determiningthe thermal conductivity of the medium in accordance with theexpression:

$k = \frac{5}{\frac{15\; \Delta \; T}{\Gamma \; \overset{\_}{a^{2}}} - \frac{1.0}{k_{b}}}$

where k is the thermal conductivity of the medium, ΔT is the meantemperature difference, a is the radius of a spherical heating meanshaving a volume equivalent to the actual volume of the heating means andk_(b) is the predetermined thermal conductivity of the heating means.

In still other embodiments, the time varying relationship between thesquare of the voltage V_(h) ² and the inverse square root of the timet.sup.-1/2 is a substantially linear relationship of the form V_(h)²(t)=m₁+m₂t^(−1/2); and the first characteristic determining meansincludes means for determining the first characteristic Γ in accordancewith the expression:

$\Gamma = \frac{m_{1}}{R_{h}\frac{4}{3}{\pi \left( \overset{\_}{a} \right)}^{3}}$

where R_(h) is the resistance of the heating means at the volume meantemperature.

Variations of these embodiments further include: means for determining asecond characteristic β in accordance with the expression:

$\beta = \frac{m_{2}}{R_{h}\frac{4}{3}{\pi \left( \overset{\_}{a} \right)}^{3}}$

memory storage means for storing the non-dimensional predeterminablerelationship between the expression β√{square root over (α_(b))}/Γāwherein α_(b) is the predetermined thermal diffusivity of the heatingmeans; the expression k_(m)/k_(b), wherein k_(m) is the thermalconductivity of the medium with no fluid flowing therein; and theexpression α_(b)/α_(m) is the thermal diffusivity of any medium which isto be determined; and means for determining the actual value of theexpression β√{square root over (α_(b))}/Γā and k_(m)/k_(b) and fordetermining the actual value of α_(b)/α_(m) from the memory storagemeans; and means responsive to the value of α_(b)/α_(m) for determiningthe thermal diffusivity α_(m) of the medium.

In other embodiments the sensing means and the heating means comprise: afirst heating element immersed at a first region of the medium; and asecond element immersed at a second region of the medium sufficientlyremote from the first region as to be not affected or minimally affectedby the heating of the first element. In certain embodiments the firstand second elements are thermistor bead elements.

Other variations for use over a relatively long time period during whichthe reference temperature varies with time and wherein the secondelement determines the reference temperature over the time period;further include: means for maintaining the volume mean temperature andthe resistance of the heating means at the volume mean temperature atfixed predetermined values over the time period during which thereference temperature varies whereby the temperature difference therebetween varies over the time period.

Variations of such embodiments have the data processing means determinethe thermal conductivity of the medium over the time period inaccordance with the expression:

${k(t)} = \frac{5}{\frac{\Delta \; {T(t)}R_{h}20\pi \; \overset{\_}{a}}{V_{h}^{2}(t)} - \frac{1.0}{k_{b}}}$

where k(t) is the thermal conductivity, ΔT(t) is the temperaturedifference, R_(h) is the resistance of the heating means at the meantemperature, V_(h)(t) is the voltage at the heating means as power isapplied thereto, a is the radius of a spherical heating means having avolume equivalent to the actual volume of the heating means and k_(b) isthe predetermined thermal conductivity of the heating means. The dataprocessing system may also include means for determining the intrinsicthermal conductivity k_(m) of the medium when no fluid is flowingtherein; means for determining the effective thermal conductivityk_(eff)(t) of the medium when a fluid having a predetermined heatcapacity is flowing therein; means for determining the ratio ofk_(eff)(t)/k_(m) over the time period; and means for determining therate of flow ω(t) of the fluid in the medium in accordance with theexpression:

${\omega (t)} = {\left( {\frac{k_{eff}(t)}{k_{m}} - 1} \right)^{2}\frac{k_{m}}{{C_{b}\left( \overset{\_}{a} \right)}^{2}}}$

where C_(b) is the predetermined heat capacity.

Other embodiments for use over a relatively long time period duringwhich the reference temperature varies with time wherein the secondelement determines the reference temperature over the time period; andmay further include means for determining the volume mean temperatureover the time period as a function of the reference temperature and apreselected fixed value of the temperature difference; means formaintaining the resistance of the first element over the time period ata value such as to maintain the temperature difference between thevolume mean temperature and the reference temperature at the preselectedfixed value, the resistance varying as a function of time; and means fordetermining the thermal conductivity of the medium over the time periodin accordance with the expression:

${k(t)} = \frac{5}{\frac{\Delta \; {T(t)}R_{h}20\pi \; \overset{\_}{a}}{V_{h}^{2}(t)} - \frac{1.0}{k_{b}}}$

where ΔT is the temperature difference, R_(h)(t) is the resistance ofthe heating means at the volume mean temperature, ā is the radius of aspherical heating means having a volume equivalent to the actual volumeof the first element, V_(h)(t) is the voltage at the first element whenpower is applied thereto, and k_(b) is the predetermined thermalconductivity of the first element. The data processing system mayinclude means for determining the intrinsic thermal conductivity k_(m)of the medium when no fluid is flowing therein; means for determiningthe effective thermal conductivity k_(eff)(t) of the medium when a fluidhaving a predetermined heat capacity is flowing therein; means fordetermining the ratio of k_(eff)(t)/k_(m) over the time period; andmeans for determining the rate of flow ω(t) of the fluid in the mediumin accordance with the expression:

${\omega (t)} = {\left( {\frac{k_{eff}(t)}{k_{m}} - 1} \right)^{2}\frac{k_{m}}{{C_{b}\left( \overset{\_}{a} \right)}^{2}}}$

where C_(b) is the predetermined heat capacity.

Still other embodiments for use over a relatively long time periodduring which the reference temperature varies with time wherein thesecond element determines the reference temperature over the timeperiod; further include means for determining the resistance of thesecond element over the time period; means for determining the desiredresistance of the first element over the time period as a function ofthe resistance of the second element and of a preselected fixed value ofthe resistance difference between the resistances of the second and thefirst elements; means for maintaining the resistance of the firstelement at the desired resistance so that the resistance difference ismaintained at the predetermined fixed value, the resistance of the firstelement varying as a function of time; means for determining the volumemean temperature of the first element over the time period at thedesired resistance of the first element, the volume mean temperaturevarying as a function of time; means for determining the temperaturedifference between the volume mean temperature and the referencetemperature over the time period, the temperature difference varying asa function of time; means for determining the thermal conductivity ofthe medium over the time period in accordance with the expression:

${k(t)} = \frac{5}{\frac{\Delta \; {T(t)}R_{h}20\pi \; \overset{\_}{a}}{V_{h}^{2}(t)} - \frac{1.0}{k_{b}}}$

where ΔT(t) is the temperature difference, R_(h)(t) is the resistance ofthe heating means at the volume mean temperature, a is the radius, of aspherical heating means having a volume equivalent to the actual volumeof the first element, V_(h)(t) is the voltage at the first element whenpower is applied thereto, and k_(b) is the predetermined thermalconductivity of the first element. The data processing system mayinclude means for determining the intrinsic thermal conductivity k_(m)of the medium when no fluid is flowing therein; means for determiningthe effective thermal conductivity k_(eff)(t) of the medium when a fluidhaving a predetermined heat capacity is flowing therein; means fordetermining the ratio of k_(eff)(t)/k_(m) over the time period; andmeans for determining the rate of flow ω(t) of the fluid in the mediumin accordance with the expression:

${\omega (t)} = {\left( {\frac{k_{eff}(t)}{k_{m}} - 1} \right)^{2}\frac{k_{m}}{{C_{b}\left( \overset{\_}{a} \right)}^{2}}}$

where C_(b) is the predetermined heat capacity.

Referring again to FIG. 7, apparatus for determining thermal propertiesof living tissue in accordance with certain preferred embodiments willbe described. An apparatus for determining properties of a medium,comprises: a computer 50; a display 52 in electrical communication withthe computer 50; a detector circuit 54 in electrical communication withthe computer 50; a printer 56 communicating with printed tape slot 63(FIG. 1) and in electrical communication with the detector circuit 54; afirst power supply 58 in electrical communication with the detectorcircuit 54; a second power supply 60 in electrical communication withthe computer 50, display 52, detector circuit 54, and printer 56; akeypad 62 in electrical communication with the detector circuit 54; anda probe 64 in electrical communication with the detector circuit 54. Incertain embodiments the apparatus further comprises an external serialport 66 in electrical communication with the detector circuit 54. Inother embodiments the apparatus further comprises an external output.This output may be either digital or analog.

The computer 50 may be any number of suitable microprocessor types,which may include optional peripheral devices for input and output ofdata. The computer illustrated is a single board microprocessor. Thepreferred computer may also comprise a first and second serial port. Thedisplay 52 may be any number of types, for example, a flat paneldisplay. The first power supply 58 is an isolated power supply and thesecond power supply 60 is an un-isolated power supply.

In a preferred embodiment, the probe 64 comprises first and secondthermistors 106 and 176, respectively, (FIGS. 8 and 9) in communicationwith a control circuit 72. One example of thermistors that can be usedwith this embodiment are B35 and BR11 manufactured by Thermometrics,Inc. (Edison, N.J.). One example of a probe including such thermistorsis shown in the above referenced U.S. Pat. No. 5,035,514. The detectorcircuit 54 comprises: an isolated component 68 comprising: a processor70, the control circuit 72 in electrical communication with theprocessor 70, and at least one analog to digital converter 74; and anun-isolated component 76, in electrical communication with the processor70 of the isolated component, comprising: a keyboard controller 78, aserial port 80, a serial port multiplexor 82, and a digital to analogconverter 84.

The control circuit 72 will be referenced in connection with FIGS. 7 and8. The control circuit serves to selectively measure temperature on orraise the temperature of the first or heat thermistor 106 of the probe64.

A circuit for a Heat Thermistor Control Circuit 72 shown in FIG. 7, isalso shown schematically in FIG. 8. The current source circuit 100measures temperature using the thermistor 106 located in the probe 64.The circuitry of box 105 is the interface of the heat thermistor controlcircuit 72 with the thermistor 106. The functionality of the controlcircuit is controlled using switches A through F. The control circuitfurther comprises first 140 and second 145 op-amps in connection with ascaling network 110, an integrator 115, control resistor 150, and acurrent source 125. The probe 64 and thermistor 106 are connected tocontrol circuit 72 through the probe interface 105, switch C and theconnector 53 shown in FIG. 1.

In a passive temperature monitoring or sense mode, referring to FIG. 8,the thermistor 106 is connected to the sense current source 100 and toground 102. Two precision resistors 150 and the 2.5 KOhm resistor shownbetween the current source and switch D are connected in series as well.The position of each switch for the sense (or unheated) mode isdescribed in Table 1-1.

TABLE 1-1 Switch Positions for Sense Mode Switch Position A right,connecting fixed resistor to thermistor B left, selecting thermistor Cright, connecting thermistor to ground D left, connecting fixed resistorto current source E up, disconnecting feedback loop F closed, opamp asamplifier not integrator

In the self-heating or heat mode, the resistor 150 and the thermistor106 are connected to the current source 125 and, once the scalingnetwork 110 is set for the desired level of amplification, the rest ofthe control loop is closed using the switches as described in Table 1-2.

TABLE 1-2 Switch Position for Heat Mode Switch Position A right,connecting fixed resistor to thermistor B left, selecting thermistor Cleft, connecting thermistor to current sink D right, connecting fixedresistor to 5 V E down, closing feedback loop F open, opamp asintegrator

Element 103, unused in both the sense and heat modes as described, is asimulator for circuit testing purposes. Switch A is moved to the leftposition only for testing purposes.

FIG. 9 shows a schematic of an embodiment of a thermal sensor and safetycircuit that comprises another part of the control circuit of theDetector Circuit 54 as shown in FIG. 7. The thermal sensor and safetycircuit consist of a current source 170 for measuring the temperaturewith the second or sense thermistor 176 of the probe 64 (FIG. 7); a setof calibration resistors 185, 190; and a safety circuit 195 that gives asignal or terminates operation if the voltage applied to thermistor 176is outside of a preset range. The second thermistor 176 connects throughthe connector 53 shown in FIG. 1.

As perfusion measurements are being taken and time passes,physiological, sensor and instrument conditions change and recalibrationis necessary. Referring again to FIGS. 3 and 4, the physiological orsensor and instrument artifact conditions are examples of conditionsthat may change and affect established baseline conditions. One or moresuch conditions are monitored and recalibration is initiated when avalue or values associated with these monitored conditions fall outsideof a predetermined range.

In the mode of FIG. 3, physiologic conditions are monitored and when theresulting value or a weighted combination of values fall within apredetermined range, that is when the monitored conditions do notmaterially affect or degrade accuracy, recalibration is not therebyindicated. One or more measurement artifact conditions are alsomonitored and when the resulting value or weighted combination of thesevalues are within a preset acceptable range, that is when perfusionmeasurement accuracy is not materially affected or degraded by artifactconditions, recalibration is again not indicated. Perfusion measurementsare deemed reliable.

When either or both of the values resulting from measurement of one ormore physiologic conditions and the values resulting from measurement ofartifact conditions fall outside of the preset ranges, indicating adegradation of accuracy of the perfusion measurements, recalibration isindicated. The perfusion sensor is calibrated in response to adegradation of accuracy due to physiologic conditions and the instrumentis calibrated in response to a degradation of accuracy due to sensor orinstrument artifact conditions that adversely affect perfusionmeasurement. Calibration and recalibration may be initiated manually inresponse to a signal provided by the system or initiated automaticallyby the system.

In the mode of FIG. 4, one or more physiologic, sensor and instrumentconditions are monitored. When the resulting value or values are withinan acceptable range, indicating reliability of perfusion measurements,perfusion measurements are made. When the resulting value or values areoutside of the acceptable range additional inquiry is indicated. Thesystem determines if instrument conditions contribute a substantialcomponent to the degradation. If not, recalibration in situ of theperfusion sensor is indicated. If so, recalibration of theinstrumentation is indicated. Calibration and recalibration of thesensor and/or the instrumentation may be initiated manually in responseto a signal provided by the system or initiated automatically by thesystem.

The present invention is described above in terms of specificembodiments. It is anticipated that other uses alterations andmodifications will be apparent to those skilled in the art given thebenefit of this disclosure. It is intended that the following claims beread as covering such other uses alterations and modifications as fallwithin the true spirit and scope of the invention.

1. A method for determining perfusion in living tissue comprising thesteps of: (1) establishing baseline criteria, comprising (A) determiningan unperturbed temperature in a capillary bed; (B) causing thetemperature in the capillary bed to change from a first unperturbedtemperature to a second temperature different from said firsttemperature for a time period, and (C) determining a value or values forone or more thermal properties in the capillary bed during a firstselected portion of said time period; (2) calculating, using a computingunit, a perfusion value for blood in the capillary bed at a secondselected portion of said time period using said thermal property valueor values, and (3) evaluating, using a computing unit, one or morephysiological and artifactual conditions to determine if baselinecriteria established by step (1) are materially affected by saidconditions and if so repeating step (1).
 2. A method for determining theperfusion of blood in a volume of tissue comprising the steps of: (1)establishing thermal baseline criteria corresponding to thermalconditions of the volume of tissue comprising determining an unperturbedtissue temperature; (2) causing the temperature of the volume of tissueto change from the unperturbed temperature to a second temperaturedifferent from the unperturbed temperature during a time interval; (3)calculating, using a computing unit, at least one of an intrinsicthermal conductivity value and a thermal diffusivity value for thevolume of tissue during a first selected portion of said time interval;(4) calculating, using a computing unit, perfusion in the volume oftissue at a second selected portion of said time interval using saidvalue; (5) determining need for new baseline criteria for the tissuecomprising evaluating one or both of physiologic and artifactconditions; and (6) repeating step (1) when indicated by step (5).
 3. Amethod for determining perfusion in a volume of tissue comprising thesteps of: (1) establishing baseline criteria, comprising (A) determiningan unperturbed temperature of the tissue; (B) causing the temperature ofthe tissue to change from a first unperturbed temperature to a secondtemperature different from said first temperature for a time period, and(C) determining a value or values for one or more thermal properties oftissue during said time period; (2) calculating, using a computing unit,a perfusion value for the tissue during said time period using saidthermal property value or values, and (3) evaluating, using a computingunit, one or more physiological and artifactual conditions to determineif baseline criteria established by step (1) are materially affected bysaid conditions and if so repeating step (1).
 4. A method according toclaim 3 wherein said thermal properties include one or both of thermalconductivity and thermal diffusivity.